How do I redirect my old domain to new?

If you have a cpanel, look for "Redirects" on the main page.

Assuming Linux?
Assuming the new site has identical pages? Or no?

.htaccess will do the trick (place this in the hosting 'root' of "olddomain.com" and it should re-direct all olddomain.com/pagename.html (or whichever page) to newdomain.com/pagename.html

Create a PLAIN TEXT (notepad/textedit) and create ONLY the above in an empty file (with no extra spacing top/bottom). Save as htaccess.txt, upload to olddomain.com's root, and rename on server to .htaccess (needs . in front, lowercase filename. Yes it's that picky)

If the new site does not have identical pages you should just do domain forwarding (registrar or cpanel should help with this : make sure it is a permanent (301) redirect)

Rules:
1) If you have an EXISTING .htaccess file, back it up.
2) Don't do testing outside of .htaccess : do only 1 htaccess change at a time and test. If something wrong, un-do it. htaccess can be harsh.
3) Short period of time (1-2 months) PR on either site will fluxtuate. Be patient with ranking and SERP's when making this drastic of a change.
4) If a corresponding page does not exist on newdomain.com that used to exist on olddomain.com, you should use a 404 redirect (also htaccess) on newdomain.com to redirect to root (www.newdomain.com) otherwise you then LOSE PR
5) Again, be careful w/ htaccess. It can break your site but usually not permanently. Not a super clear syntax for htaccess (but usually easy to go to google and find an answer)

If you use cpanel hosting, in the box that says domains, there's an icon for redirects. That should do it for you. I also check the boxes: Redirect with or without www and wildcard redirect.